The new cultivar of blackberry called ‘APF-45’ is described herein. The new cultivar originated from a hand-pollinated cross of Ark. Selection APF-1×APF-12 made in 2000. The seeds resulting from this controlled hybridization were germinated in a greenhouse in the spring of 2001 and planted in a field near Clarksville, Ark. (West-Central Arkansas). The seedlings fruited in the summer of 2002 and one seedling, designated APF-45, was selected for its very firm fruit with excellent postharvest handling potential, medium-large size, attractive fruit appearance, very good flavor, excellent plant health, and cane erectness.